MthSc 208, Spring 2011 (Differential Equations)
Dr. Macauley
HW 1
Due Friday January 21st, 2010
(1) Let
P
(
t
) be the net worth of an investment after
t
years, that is growing at a 5% rate.
Suppose that after two years, the investment is worth $200. Write down an
initial value
problem
(the differential equation & initial condition) for
P
, and sketch its solution.
(2) Let
T
(
t
) be the temperature of a cup of water
t
minutes after being placed in a room
where the ambient temperature is 72
◦
.
(a) Write down a differential equation that
T
satisfies.
(b) Sketch the solution curve of the solution satisfying
T
(0) = 100.
(c) Sketch the solution curve of the solution satisfying
T
(0) = 40.
(d) Sketch the solution curve of the solution satisfying
T
(0) = 72.
(3) Repeat the previous exercise, except let
T
(
t
) be the temperature of a sheet of metal (which
cools down and heats up
much
quicker than water). Qualitatively, what is the difference
between the solution curves in these two problems? Which value of
k
is bigger and why?
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 Spring '09
 Staufeneger
 Differential Equations, Equations, 5%, $200, Two years, Dr. Macauley HW

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